To solve the equation $a + b - c = \frac{r}{m}$ for $b$, follow these steps:

1. Start with the original equation: $a + b - c = \frac{r}{m}$

2. To isolate $b$, first add $c$ to both sides of the equation: $a + b = \frac{r}{m} + c$

3. Next, subtract $a$ from both sides: $b = \frac{r}{m} + c - a$

So, the equation solved for $b$ is: $b = \frac{r}{m} + c - a$

Would you like more details on this, or do you have any other questions?

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Here are 5 related questions to consider:

1. How would the expression for $b$ change if $m$ were to equal 1?
2. What is the value of $b$ if $r = 0$?
3. How does changing $a$ affect the value of $b$?
4. What would the equation look like if you doubled the value of $c$?
5. Can you express $b$ in terms of $m$ if $r$ is dependent on $m$?

Tip: When isolating a variable, ensure you perform the operations step-by-step to maintain the equation's integrity.